On the size of the set A(A + 1)
Journal
Mathematische Zeitschrift
Journal Volume
265
Journal Issue
1
Pages
125-132
Date Issued
2010
Author(s)
Garaev, M.Z.
Abstract
Let Fp be the field of a prime order p. For a subset A ⊂ Fp we consider the product set A(A + 1). This set is an image of A × A under the polynomial mapping f(x, y) = xy + x: Fp × Fp → Fp. In the present note we show that if {pipe}A{pipe} < p1/2, then, If {pipe}A{pipe} > p2/3, then we prove that, and show that this is optimal in general settings bound up to the implied constant. We also estimate the cardinality of A(A + 1) when A is a subset of real numbers. We show that in this case one has the Elekes type bound,. © Springer-Verlag 2009.
SDGs
Type
journal article